Contemporary footbridges, due to their slender and lightweight structural characteristics, are prone to human-induced vibrations. This paper proposes a vibration mitigation strategy for lively footbridges under walking-induced excitations, which are modeled as moving harmonic loads, by employing nonlinear vibration absorbers. Firstly, a novel vertical polynomial stiffness nonlinear vibration absorber (VPNVA) incorporating a gravity compensation mechanism is proposed. Experiments on the stand-alone VPNVA indicate that the implementation scheme enables the effective realization of polynomial stiffness, with frequency responses of the VPNVA showing good agreement with theoretical predictions. Secondly, the response regimes of the system, consisting of two VPNVA devices installed on both sides at the midspan of a lively footbridge, are analyzed with consideration of multi-modal vibrations. The results show that the vibrations on both sides of the footbridge may evolve along the lower branch of the slow invariant manifold (SIM), both may jump from the lower branch to the upper branch, or, one side may remain along the lower branch while the other jumps to the upper branch when both bending and torsional mode vibrations are included. Finally, the VPNVA with optimal stiffness coefficients and a low damping coefficient demonstrates effective vibration suppression, and the performance is further improved with additional optimal damping. Under detuning conditions where both bending and torsional modes fall within the walking excitation frequency range, the optimally designed VPNVA still maintains satisfactory vibration suppression performance, indicating its effectiveness in controlling multi-modal vibrations, even with frequency detuning. Compared with the conventional TMD, the VPNVA exhibits lower sensitivity to stiffness variations under low damping conditions. The proposed VPNVA provides an effective approach to vibration control of large-scale structures under moving loads.
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